A solution with PSTricks only for either fun or comparison purposes.

curvepnodes is useful to define an array of nodes for any given number of nodes and curve functions. For example, we can use it to make an array of 12 nodes on a circle. Offset is provided as the rotation offset.

documentclass[pstricks,margin=5mm]{standalone}
usepackage{pst-node,pst-plot}

begin{document}
begin{pspicture}[showpoints,dotscale=1](-4,-4)(4,4)
    pstVerb{/Offset 30 def}%
    curvepnodes[plotpoints=11]{0}{360}{3 t Offset add PtoC}{A}
    psnpolygon[linecolor=red](0,numexprAnodecount-1){A}
end{pspicture}
end{document}

Animated version

documentclass[pstricks,margin=5mm]{standalone}
usepackage{pst-node,pst-plot}

begin{document}
multido{i=0+10}{10}{%
begin{pspicture}[showpoints,dotscale=6](-4,-4)(4,4)
    pstVerb{/Offset ispace def}%
    curvepnodes[plotpoints=13]{0}{360}{3 t Offset add PtoC}{A}
    psnpolygon[linecolor=red](0,numexprAnodecount-1){A}
end{pspicture}}
end{document}

In this link you can find a series of regular polygons...I have changed the code to have the penthagon. Here the drawing is without coordinates.

documentclass[12pt]{article}
usepackage{tikz}
begin{document}
% Radius of regular polygons
newdimenR
R=1cm
This is a pentagon $n=10$, 
begin{tikzpicture}
    draw[yshift=-6.0R] (0:R) foreach x in {36,72,...,359} {
            -- (x:R)
        } -- cycle (90:R) node[above] {$scriptstyle n=10$} ;
end{tikzpicture}
that it could be used as a symbol. 
end{document}